Magnetic field sensors are ubiquitous, they are found as position, rotation and velocity sensors in vehicles and industrial equipment. They are also used for current sensing in high power applications and the advance in magnetic sensors has enabled the low-cost high-density hard disk industry.
For magnetic sensors to be attractive they need to have a high magnetoresistance (MR>100%), have a linear response in a small magnetic field (%/Oe), and have low resistance (high signal to noise).
Presently, magnetic sensors have high magnetoresistance (MR>100%), for example MgO based magnetic tunnel barriers, but these have a high resistance due to the nature of the tunnel barrier. Hall sensors are cheap and have a linear response but a very low sensitivity (%/Oe). Anisotropic magneto resistance sensors have low resistance and thus high signal to noise but very low magnetoresistance (MR<2-3%).